The prior art does not provide a satisfactory valve apparatus which may serve as an inside blowout preventer for use in a drill string, or which may be used as a float valve above the drilling bit in wire line coring operations, or which may be used as an upper and/or lower cock in connection with a Kelly for the purpose of minimizing use of drilling mud, or which may be used as a subsurface safety valve having a fail-safe hydraulic latch-open arrangement, or which may be employed in any other standard check valve applications in hydraulic and pneumatic systems, and which may be used in pipelines, in chemical and other processing, and in petroleum production. The valves for these purposes available in the art are subject to failure by reason of the presence of detritus or suspended solids in the flowing fluid, by reason of abrasion-cutting of valve seats and other parts, by reason of corrosion, or by reason of excessive temperature elevation of the flowing fluid. The invention provides methods through use of which the above described problems are eliminated, and in addition provides apparatus, in plural modifications, which may be utilized in accordance with the methods.